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arXiv · 1912.06925

On the characterization of the space of derivations in evolution algebras

Yolanda Cabrera Casado·Paula Cadavid·Mary Luz Rodiño Montoya·Pablo M. Rodriguez
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Abstract

We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph we prove that the space of derivations is zero. For the remaining families of evolution algebras we obtain sufficient conditions under which the study of such a space can be simplified. We accomplish this task by identifying the null entries of the respective derivation matrix. Our results suggest how strongly the associated graph's structure impacts in the characterization of derivations for a given evolution algebra. Therefore our approach constitutes an alternative to the recent developments in the research of this subject. As an illustration of the applicability of our results we provide some examples and we exhibit the classification of the derivations for non-degenerate irreducible $3$-dimensional evolution algebras.

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Yolanda Cabrera Casado, Paula Cadavid, Mary Luz Rodiño Montoya, Pablo M. Rodriguez. 2019-12-14. On the characterization of the space of derivations in evolution algebras. https://arxiv.org/abs/1912.06925

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